Evaluation of Two Alternative Methods to Calibrate ... - Semantic Scholar

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 3, MARCH 2011

965

Evaluation of Two Alternative Methods to Calibrate Ultrahigh Value Resistors at INRIM Flavio Galliana, Pier Paolo Capra, and Enrico Gasparotto

Abstract—In the framework of the preparation of the National Institute of Metrological Research (INRIM) to its participation at the “Supplementary Comparison EURAMET.EM-S32 Comparison of Resistance Standards at 1 TΩ and 100 TΩ,” an evaluation of two measurement techniques for high resistance measurements at INRIM has been made. The first method, working between 10 MΩ and 1 TΩ, is based on a digital multimeter and on a dc voltage (dcv) calibrator, the second, working up to 100 TΩ, is based on a modified Wheatstone bridge with two programmable dcv calibrators in two arms of the bridge and a programmable electrometer as null detector. A description of both methods, a detailed uncertainties budget at 1 TΩ at 1000 V level according to the ISO Guide to the Expression of Uncertainty in Measurements, and the comparison of the results at 100 GΩ and at 1 TΩ are reported. Index Terms—Compatibility of the measurements, guarding system, measurement model, measurement uncertainties, resistance measurement method, ultrahigh value resistor.

I. I NTRODUCTION

I

N THE PAST YEARS, in the field of high dc resistance, the National Institute of Metrological Research (INRIM), formerly the “Istituto Elettrotecnico Nazionale Galileo Ferraris” (IEN), developed and characterized a measurement method based on a digital multimeter (DMM) dc voltage (dcv) calibrator to be used for the calibration of standard resistors mainly in the range from 10 MΩ to1 TΩ[1]. This method is also suitable for determining the voltage coefficients of highvalue resistors [2]. Using this method and a Hamon scaling method, [3] the IEN participated at a Consultative Committee for Electricity and Magnetism (CCEM) intercomparison on 10 MΩ and 1 GΩ values. The degrees of equivalence of IEN, expressed as differences from the reference values XKCRV (Key Comparison Reference Value), resulted 0.9 ± 5.5 × 10−6 and 2.5 ± 19.3 × 10−6 , respectively, at 10 MΩ and 1 GΩ[4]. Another well-known and reliable measurement method for the calibration of high-value resistors is the modified Wheatstone-bridge-based measurement system, developed at the National Physical Laboratory (NPL UK) [5] at the National Institute of Standards and Technology (NIST USA) in guarded [6] and with dual balance [7] versions and at the PhysikalischTechnische Bundesanstalt (PTB DE) [8]. In the following, the implementation of both methods at the INRIM in the framework of the Comparison EURAMET.EM-S32, a detailed

Manuscript received March 25, 2010; revised May 24, 2010; accepted June 4, 2010. Date of publication August 9, 2010; date of current version February 9, 2011. The Associate Editor coordinating the review process for this paper was Dr. Rik Pintelon. The authors are with the National Institute of Metrological Research, 10135 Torino, Italy (e-mail: [email protected]; [email protected]; e.gasparotto@ inrim.it). Digital Object Identifier 10.1109/TIM.2010.2060226

Fig. 1. Detailed scheme of the DMM-dcv calibrator measurement method.

uncertainties budget of the two methods according to the ISO Guide to the Expression of Uncertainty in Measurement at 1 TΩ at 1000 V level, a compatibility test between them and some adjunctive considerations are reported. II. DMM-DCV C ALIBRATOR M ETHOD The DMM-dcv calibrator measurement method is usually utilized for the calibration of high-value resistors in the range 10 MΩ to 1 TΩ. A scheme of this measurement system is shown in Fig. 1. Rx is the resistor under calibration and Rs is the reference resistor. An auxiliary resistive divider provides a guard voltage. For this guard voltage, a Kelvin-Varley voltage resistive divider was actually utilized. Its ratio Z is always chosen so that Z ∼ = Rx /Rs . More details of the method are reported in [1]. The dcv calibrator supplies a positive voltage Vout to the series of Rx and Rs , while the DMM measures the voltage Vs on Rs . After a set number of measurements, the polarity of Vout is reversed and Rx is the mean value of Rx+ and Rx . From Fig. 1, being Vx , the voltage on Rx and Ix the current through Rx and Rs , the value of Rx is given by Vx Rx = Ix RS = (Vout −Vs ) Vs  Vout = Rs −1 VS   Vout +kcal−cal +kCal−acc ∼ −1 = Vs +kDM M −cal +kload +kDM M −acc +kterm−bias  × (RS kdrif t kT ) kleak krepeat kAx

0018-9456/$26.00 © 2010 IEEE

(1)

966

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 3, MARCH 2011

where Rs Vout

Vs kdrift ∼ =1 kT ∼ =1 kload ∼ =0V kDM M −cal ∼ =0V kDM M −acc ∼ =0V kcal−cal ∼ =0V kcal−acc ∼ =0V kterm−bias ∼ =0V

kleak ∼ =1 krepeat ∼ =1

kAx ∼ =1

is the reference resistor and is the voltage supplied by the dcv calibrator. As uncertainty contribution, its midterm instability, as declared by the manufacturer, was taken into account. is voltage on Rs read by the DMM. For this quantity, its type A standard uncertainty was taken into account. is the corrective term to take into account the drift of Rs ; is corrective term to take into account the instability of Rs due to temperature instability; is corrective term to take into account the error due to the DMM input impedance; is the corrective term to take into account the error in the calibration of the DMM; is corrective term to take into account the accuracy of the DMM; is the corrective term to take into account the error in the calibration of the dcv calibrator; is corrective term to take into account the accuracy of the calibrator; is corrective term to take into account the error of the DMM due to effects of bias current and of thermal and offset voltages residual to polarity inversion; is corrective term to take into account the error due to the leakages; and is corrective term to take into account the repeatability of Rx . For this quantity its type A standard uncertainty was taken into account; corrective term to take into account the instability of Rx due to instability of environment conditions during the measurements.

Fig. 2.

I(0+) and I(0−) at the picoammeter at the voltages Vsd1 and Vsd2 , respectively. Then, with a linear fit, Vsd at I = 0 is evaluated. The procedure is then repeated for the reverse values Vxr and Vsr to evaluate Vsr at I = 0. Finally, Vx and Vseq at the bridge balance are evaluated as Vseq = Vx =

|Vsd | + |Vsr | 2

(2)

|Vxd | + |Vxr | . 2

(3)

The value of Rx is given by    Vx +kcalhi−acc +kcalhi−cal −Vb Rx ∼ = Rs (kdrif t kT kV ) (Vs +kcallo−acc +kcallo−cal −Vb ×kdet kint krepeat kconn kleak kAx

(4)

where

A corrective term to take into account the voltage dependence of RS was not inserted because in its characterization, Rs did not show any dependence from the applied voltage.

Rs Vx

III. M ODIFIED W HEATSTONE B RIDGE M ETHOD

Vs

As shown in Fig. 2, in this modified Wheatstone bridge, two resistive arms are replaced by two programmable low-impedance voltage calibrators. The null detector is a picoammeter ideally considered with internal resistance ∼ = 0. The traceability of this method at INRIM starts from a 10 GΩ standard resistor calibrated with the DMM-dcv calibrator method and follows to higher decade values in the 1:10 step-up ratio. The adopted automatic measurement procedure consists of setting the nominal direct voltages Vxd supplied by the Hi calibrator and Vsd supplied by the Lo calibrator so that Vxd /(−Vsd ) ∼ = Rx /Rs . Then, Vsd is automatically adjusted to obtain close to 0 successively positive and negative values

Detailed coaxial setup of the modified Wheatstone bridge method.

kdrift ∼ =1 kT ∼ =1 kV ∼ =1 kdet ∼ =1

is the reference resistor and is the voltage supplied by the Hi calibrator. As uncertainty contribution, its midterm instability, as declared by the manufacturer, was taken into account. is the voltage supplied by the Lo calibrator at the balance of the bridge. For this quantity, its type A standard uncertainty was taken into account. is the corrective term to take into account the drift of Rs ; is the corrective term to take into account the instability of Rs due to instability of temperature; is the corrective term to take into account the voltage dependence of Rs ; is the corrective term to take into account the resolution of the detector;

GALLIANA et al.: EVALUATION OF TWO ALTERNATIVE METHODS TO CALIBRATE ULTRAHIGH VALUE RESISTORS

967

TABLE I UNCERTAINTIES BUDGET AT 1 TΩ AT 1000 V OF THE DMM–dcv CALIBRATOR METHOD

kint ∼ =1

is the corrective term to take into account the interpolation of the readings of the detector; and 1 is the corrective term to take into account krepeat ∼ = the repeatability of Rx . For this quantity, its type A standard uncertainty was taken into account. is the corrective term to take into account kAx ∼ =1 the instability of Rx due to instability of environment conditions; is the corrective term to take into account kconn ∼ =1 the error due to the connections; is the corrective term to take into account kleak ∼ =1 the error due to the leakages; kcalhi−cal ∼ = 0 V is the corrective term to take into account the error in the calibration of the Hi dcv calibrator; kcalhi−acc ∼ = 0 V is the corrective term to take into account the accuracy of the Hi dcv calibrator; kcallo−cal ∼ = 0 V is the corrective term to take into account the error of the calibration of the Lo dcv calibrator; ∼ 0 V is the corrective term to take into account kcallo−acc = the accuracy of the Lo dcv calibrator; and is the estimate of the voltage burden of the Vb detector [9] and of the residual effects to the polarity inversion of offset and thermal voltages.

IV. D ETAILED U NCERTAINTIES B UDGETS AT 1 TΩ L EVEL The participation at the Supplementary Comparison EURAMET.EM-S32 was also the occasion to review the uncertainties of the methods with respect to those in [1]. As an example, in Tables I and II, detailed budgets according to the ISO Guide to the Expression of Uncertainty in Measurements [10] at 1 TΩ level at 1000 V, respectively, with the DMM-dcv calibrator method and with the modified Wheatstone bridge method, are reported. All input quantities are considered to be independent. V. C OMPARISON OF THE M ETHODS The DMM and the three calibrators utilized in the two measurement setups were previously calibrated by the INRIMLab for calibration of high-precision multifunction instruments [11]. The calibration system of the INRIM-Lab consists of a group of reference standards such as a 10-V Zener voltage reference standard, two resistive voltage dividers, a set of standard resistors and shunts, and a programmable ac/dc voltage transfer standard, which are periodically calibrated versus the national standards. The INRIM-Lab typically calibrates high-stability DMMs, multifunction calibrators, and dc voltage calibrators, and them compares them with reference standards. To check the compatibility between the two methods, one 100 GΩ and three 1 TΩ resistors were measured with both systems. The scheme of these resistors is shown in Fig. 3. In these resistors, the required resistance value is achieved by a

968

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 3, MARCH 2011

TABLE II UNCERTAINTIES BUDGET AT 1 TΩ AT 1000 V OF THE MODIFIED WHEATSTONE BRIDGE METHOD

Fig. 3. Measured standards, one 100 GΩ and three 1 TΩ.

resistance network. Assuming that the output terminal and the shield are at the same potential, the resistance Rx between the source and output terminal is given by   Ri Rx = Ri + R0 1 + . (5) Rd With the DMM-dcv calibrator method, the shield of one terminal of the resistors under calibration and the shield of the reference resistor were connected to the guard point (Fig. 1), while with the modified Wheatstone bridge method, the shield of one terminal of both the reference and the under calibration resistors were connected to the ground (Fig. 2). To perform the measurements with the DMM-dcv calibrator method, an accurate balancing of the guard voltage annulling the residual voltage between the guard point and the low terminal of Rx by means of a null detector D and acting on the resistive divider (Fig. 1) was done. A 10 MΩ standard resistor was

involved as Rs . Moreover, an accurate determination of the input impedance of the involved DMM, which resulted better than 1 × 1012 Ω, was done. In the modified Wheatstone bridge method, the reference and under calibration resistors were both placed in a metallic shield box (dashed lines in Fig. 2). The measurements with both systems were carried out in the INRIM resistance laboratory, normally regulated at (23 ± 0.3) ◦ C and with relative humidity at (40 ± 10)%. The reference and under calibration resistors of both systems were placed in air thermostatic baths at a temperature of (23 ± 0.1) ◦ C. Both measurement setups were managed by battery-supplied portable computers to minimize noise. The mean values of the measurements are shown in Figs. 4–7. The results shown in Figs. 4–7 are in good agreement within the respective uncertainties. The agreement must be taken with some care since there is some degree of correlation between the two methods (essentially due to the calibration of the 10 GΩ resistor). A full evaluation of the uncertainty of such comparison would require one to take into account such correlation, which is beyond the aim of this paper. A full validation of the methods will come from the results of the Comparison EURAMET.EMS32 Comparison of Resistance Standards at 1 TΩ and 100 TΩ. With the DMM-dcv calibrator method, the spread of the measurements significantly increased lowering the applied measurement voltage with respect to the other method, as the voltage that the DMM reads on the reference resistor decreases.

GALLIANA et al.: EVALUATION OF TWO ALTERNATIVE METHODS TO CALIBRATE ULTRAHIGH VALUE RESISTORS

Fig. 4. Results on the 100 GΩ resistor with both methods. The measurements were carried out at 100 V, 500 V, and 1000 V, but in the graph are reported at little different voltages between the two methods to better distinguish their 2σ uncertainty bars.

969

Fig. 7. Results on the third 1 TΩ resistor with both methods. The measurements were carried out at 100 V, 500 V, and 1000 V, but in the graph are reported at little different voltages between the two methods to better distinguish their 2σ uncertainty bars.

Another interesting fact is that in all the measurements, the results with the modified Wheatstone bridge method have lower values with respect to those with the other method. Presumably, the reason is that the DMM-dcv calibrator method is a fully guarded method, while in the other method, the high side of the detector is not guarded as in [6], [7]. As a matter of fact, guarding the high side of the detector reduces leakages at that point, which could cause a little shift of the balance of the bridge, thereby causing lower measured resistance values. VI. C ONCLUSION

Fig. 5. Results on the first 1 TΩ resistor with both methods. The measurements were carried out at 500 V and 1000 V, but in the graph are reported at little different voltages between the two methods to better distinguish their 2σ uncertainty bars.

The evaluation of two alternative measurement methods for the calibration of ultrahigh value resistors involved at the INRIM for the measurement of the Supplementary EURAMET.EM-S32 comparison was reported. The comparison between the two methods showed satisfactory agreement between them. Future aim will be implementation of a full guarding system for the modified Wheatstone bridge method to extend the INRIM dc resistance capabilities up to 1–10 PΩ. ACKNOWLEDGMENT The authors would like to thank L. Callegaro of INRIM for his precious advice in the setup of the modified Wheatstone bridge circuit. R EFERENCES

Fig. 6. Results on the second 1 TΩ resistor with both methods. The measurements were carried out at 500 V and 1000 V, but in the graph are reported at little different voltages between the two methods to better distinguish their 2σ uncertainty bars.

[1] F. Galliana, P. P. Capra, and E. Gasparotto, “Metrological management of the high dc resistance scale at INRIM,” Measurement, vol. 42, no. 2, pp. 314–321, Feb. 2009. [2] G. Boella and F. Galliana, “Analysis of voltage coefficients of high value standard resistors,” Measurement, vol. 41, no. 1, pp. 1–9, Jan. 2008. [3] B. V. Hamon, “A 1–100 Ω build-up resistor for the calibration of standard resistors,” J. Sci. Instrum., vol. 31, no. 12, pp. 450–453, Dec. 1954. [4] R. F. Dziuba and D. G. Jarrett, “Final report on key comparison CCEMK2 of resistance standards at 10 MΩ and 1 GΩ,” Metrologia, vol. 39, p. 01 001, 2002. DOI: 10.1088/0026–1394/39/1A/1. [5] L. C. A. Henderson, “A new technique for the automatic measurement of high value resistors,” J. Phys. E, Sci. Instrum., vol. 20, no. 5, pp. 492–495, May 1987. [6] D. G. Jarrett, “Automated guarded bridge for calibration of multimegohm standard resistors from 1 MΩ to 1 TΩ,” IEEE Trans. Instrum. Meas., vol. 46, no. 2, pp. 325–328, Apr. 1997.

970

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 60, NO. 3, MARCH 2011

[7] D. G. Jarrett, “Analysis of a dual-balance high-resistance bridge at 10 TΩ,” IEEE Trans. Instrum. Meas., vol. 50, no. 2, pp. 249–254, Apr. 2001. [8] B. Schumacher, E. Pesel, and P. Warnecke, “Traceability of high-value resistance measurements at PTB,” in Proc. 9th Int. Metrol. Conf., 1999, pp. 52–55. [9] P. P. Capra, F. Galliana, and E. Gasparotto, “A measurement setup to calibrate picoammeters in the range 1 nA ÷ 1 μA and to estimate the voltage burden,” in Proc. 14th Int. Metrol. Conf., 2009, [CD-ROM], file code 171.swf. [10] BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, Guide to the Expression of Uncertainty in Measurement1993. [11] C. Cassiago, G. La Paglia, and U. Pogliano, “Stability evaluation of highprecision multifunction instruments for traceability transfer,” IEEE Trans. Instrum. Meas., vol. 50, no. 6, pp. 1206–1210, Dec. 2000.

Flavio Galliana was born in Pinerolo, Torino, Italy, in 1966. He received the degree in physics from the Università di Torino, Torino, in 1991. Since 1993, he has been with the Istituto Elettrotecnico Nazionale “Galileo Ferraris” [now the National Institute of Metrological Research (INRIM)], Torino, where he is involved in precision highresistance measurements with the development and characterization of some measurement methods. He also joined the “Accreditation of Laboratories” Department of INRIM, with particular attention in the evaluation of the quality systems of the applicant laboratories and SIT calibration centers. From 2001 to 2005, he was Responsible of the “Accreditation of Laboratories” Department of IEN. Since 2006, with the constitution of INRIM, he has been involved in precision resistance measurements.

Pier Paolo Capra was born in Torino, Italy, in 1965. He received the technical high school degree in chemistry in 1984 and the degree in physics from the Università of Torino, Torino, in 1996. Since 1987, he has been with the Istituto Elettrotecnico Nazionale “Galileo Ferraris” [now the National Institute of Metrological Research (INRIM)], Torino, where he is involved in dc voltage and resistance precision measurement. Since 1997, he has been involved in the realization and maintenance of the national standard of dc electrical resistance. In 2001, he became a Researcher. Now, he is the responsible for the national resistance standard and for the dissemination of the resistance unit.

Enrico Gasparotto was born in Torino, Italy, in 1967. He received the high school degree in electronics in 1988. From 1991 to 1997, he worked in private companies, and in 1997, he joined the Electrical Metrology Department, Istituto Elettrotecnico Nazionale “Galileo Ferraris” [now the National Institute of Metrological Research (INRIM)], Torino, where he has since been involved in resistance precision measurements. Since 2008, he has been engaged in the realization of the quantum Hall effect for the reproduction of national resistance standard.